Genetic Crosses and Sex Determination

One allele from each parent

During sexual reproduction, a sperm and an egg join at fertilisation. These gametes are sex cells with one set of chromosomes. For a gene involved in a simple inheritance cross, each gamete carries just one allele—a version of that gene. The offspring therefore receives two alleles: one from each parent.

The combination of alleles is its genotype. The characteristic produced, such as a pea plant being tall or short, is its phenotype. Genetic diagrams connect these two ideas: they show which allele combinations offspring could inherit, then help us predict their characteristics.

How dominant and recessive alleles affect a characteristic

Some characteristics follow single-gene inheritance. A useful example is pea plant height, studied by Gregor Mendel. In this example, the allele for tall plants is dominant and the allele for short plants is recessive. We use T for the dominant allele and t for the recessive allele.

A dominant allele affects the phenotype even when only one copy is present. A recessive allele affects the phenotype only when two copies are present, with no dominant allele.

Homozygous means that the two alleles of a gene are identical. Heterozygous means that they are different. A heterozygous plant still carries the recessive allele and can pass it to offspring, even though the plant itself is tall.

Building a Punnett square

A Punnett square organises the possible combinations of parental alleles. Start with the parents’ genotypes, work out the alleles their gametes can carry, and place these around the outside of the square. Each box inside combines one allele from each parent.

First, cross a homozygous tall plant with a short plant: $TT \times tt$. Every gamete from the tall parent carries T, and every gamete from the short parent carries t.

All possible offspring are Tt, so all are tall. Although each parent has two alleles, each passes on only one.

Now cross two of these heterozygous plants: $Tt \times Tt$. Each parent produces gametes carrying either T or t, with equal probability.

There are four equally likely combinations: one TT, two Tt and one tt. The genotype ratio is therefore $1\,TT : 2\,Tt : 1\,tt$. Both TT and Tt plants are tall, so the phenotype ratio is $3\text{ tall} : 1\text{ short}$.

A different cross produces a different prediction. For $Tt \times tt$, one parent produces T or t gametes, while the other produces only t gametes.

Half the combinations are Tt and half are tt: the predicted phenotype ratio is 1 tall : 1 short.

Turning a cross into a probability or expected number

For equally likely boxes in a Punnett square:

$$\text{Probability of an outcome} = \frac{\text{number of boxes with that outcome}}{\text{total number of boxes}}$$

In the $Tt \times Tt$ cross, the probability of a short offspring is $1/4$, or 25%. The probability of a tall offspring is $3/4$, or 75%.

Direct proportion lets us use this probability to predict numbers. Suppose the cross produces 80 offspring. The expected number of short plants is $80 \times 1/4 = 20$, and the expected number of tall plants is $80 \times 3/4 = 60$.

These are expected numbers, not a guarantee. Fertilisation involves chance, so actual results can differ. Each offspring is a new event: getting a short plant does not make a tall plant more likely next time. Four offspring do not necessarily include exactly three tall plants and one short plant.

Following inheritance through a family

A family tree, also called a pedigree, traces a characteristic across generations. Squares usually represent males and circles females. A line joins two parents, with offspring linked below them. Always read the key to see how the characteristic is marked.

Suppose a condition is caused by a recessive allele, a, and A is dominant. Two parents without the condition have a child with the condition. The child must be aa, so each parent supplied an a allele. Since neither parent has the condition, both must be Aa: they carry the recessive allele without showing its effect.

A cross of $Aa \times Aa$ then predicts a $1/4$ probability of the condition in each child. The family tree helps infer the parental genotypes; the Punnett square predicts possible future outcomes.

Why most characteristics are more complicated

Most phenotypic features depend on multiple genes, rather than one gene with a simple dominant–recessive pair of alleles. This is called polygenic inheritance. Eye colour, for example, involves several genes and has more possibilities than just brown or blue.

A single-gene Punnett square is therefore useful for particular inheritance patterns, but it cannot fully predict most characteristics. Environmental influences can also contribute to phenotype.

Sex determination in humans

Humans usually have 23 pairs of chromosomes. One pair consists of the sex chromosomes: females typically have XX and males typically have XY.

Egg cells carry an X chromosome. Sperm cells carry either X or Y. At fertilisation, an X-bearing sperm produces XX, while a Y-bearing sperm produces XY.

The usual prediction is 1 XX : 1 XY, giving approximately a 50% probability of either outcome at each fertilisation. It is the chromosome carried by the fertilising sperm that determines which combination forms.

The chromosomes affect development through the genes they carry. Genes on the Y chromosome trigger the development of testes; a key example is SRY. This connects the inheritance of a sex chromosome to the development of biological sex, rather than treating X and Y as labels alone.

Single-gene inheritance

• Each offspring receives one allele from each parent’s gamete.
• Homozygous: identical alleles. Heterozygous: different alleles.